Santiago is eight years younger than Juan is today. If, in four years, Santiago will be half Juan’s age, how old is Santiago today? a) 1 b) 2 c) 3 d) 4

Answers

Answer 1

Answer:

d) 4.

Step-by-step explanation:

Let Santiago be x years old today.

Then Juan is x + 8 years old.

In 4 years Santiago will be x + 4 years.

In 4 years Juan will be x + 12 years.

From the given information:

x + 4 = 0.5(x + 12)

x = 0.5x + 6 - 4

0.5x = 2

x = 2 / 0.5

x = 4.

Answer 2
Let S be Santiago’s age
Let J be Juan’s age.

Since Santiago is 8 yrs younger than Juan, we can write

Equation 1: S = J-8

In 4 yrs, Santiago age will be S + 4,
In 4 yrs, Juan’s age will be J + 4.

Given:
In 4 yrs, Santiago will be half of Juan’s age, so ..

Equation 2: S+4=(J+4)/2

We know the value of S from equation 1. Substitute S=J-8 in equation 2, we get

J -8 + 4=(J+4 )/2

J-4 = (J+4 )/2

2( J- 4) =J + 4
2J-8 =J + 4
2J-J =8+ 4
J = 12

Substitute J= 12 in equation 1
S= 12-8
S = 4

So, Santiago’s age is 4 yrs today.

Related Questions

Which of the following is a graph of f(x) =square root of x +5

Answers

Answer:

Step-by-step explanation:

You didn't include any graphs, so I can't tell you which one it is. However, the graph of [tex]f(x)=\sqrt{x+5}[/tex] looks like this:

Hope this helps!

The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below and this can be determined by using the rules of transformation.

Given :

[tex]\rm f(x) = \sqrt{x+5}[/tex]

The following steps can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex]:

Step 1 - The rules of transformation can be used in order to sketch the graph [tex]\rm f(x) = \sqrt{x+5}[/tex].

Step 2 - First draw the graph of [tex]\sqrt{x}[/tex] which is in the shape of a parabola.

Step 3 - Now, translate the graph in the left direction, So the function of the graph obtained is [tex]\rm f(x) = \sqrt{x+5}[/tex].

The graph of the function [tex]\rm f(x) = \sqrt{x+5}[/tex] is attached below.

For more information, refer to the link given below:

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Which of the following describes a compound event?

Answers

Answer:

B.

Step-by-step explanation:

A compound event is the combination of two or more simple events (with two or more outcomes). The probability of drawing a heart, replacing the card, then drawing a spade. In a compound event, the numerator ("number of times it can occur") will be greater than 1.

hi the answer is B!!!!!

On a map’s coordinate grid, Panthersville is located at (−3, 2), and Heel City is located at (4, 8). Falconton is the midpoint between Panthersville and Heel City. What is the approximate distance from Panthersville to Falconton? (Each unit on the grid represents 1 mile.) A. 3.25 miles B. 4.61 miles C. 5.00 miles D. 9.22 miles

Answers

Answer:

The approximate distance from Panthersville to Falconton is: B: 4.61 miles.

Step-by-step explanation:

Objective: Find the distance from Panthersville to Falconton. (Which is just half of the distance from Panthersville to Heel City because Falconton is the midpoint between both cities.)

First we need to find the distances from Panthersville to Heel City, which we are given the coordinates. ( Panthersville (-3,2) & Heel City (4, 8) )

-To find the distance between the two cities we use the distance formula:

d= √(x2 - x1) ^2 + (y2 - y1)^2 , so we set (-3,2) as x1 and y1 while (4,8) x2 and y2 and we just plug it in.

Once we plug it in we get:

d= √(4 - -3)^2 + (8 - 2) ^2

Then we solve the numbers in the parenthesis  (4 - -3) = 7 and (8 - 2) = 6 so now we have:

d= √(7)^2 + (6) ^2

Next we solve for the exponents  (7)^2 = (7 x 7 = 49) and (6)^2 = ( 6 x 6= 36) now it look like this:

d= √49 + 36

After that we just add both numbers together (49 + 36) = 85

d= √85

Now all we have to do is square root 85 which is just 9.219544457, just round it to the nearest hundredth and you will get 9.22.

So the distance from Panthersville to Heel City is about 9.22 miles.

Now we found the full distance we now need to find the distance from  Panthersville to Falconton which is just half of that distance due to   Falconton being the midpoint.  

All we have to do is divide 9.22 by 2 and we get 4.61.

The distance from Panthersville to Falconton is 4.61 miles.

What is - 15 +6f = 5

Answers

Answer:

f = 10/3

Step-by-step explanation:

-15 + 6f = 5

-15 + 15 + 6f = 5 + 15

6f = 20

6f/6 = 20/6

f = 20/6 = 10/3 = 3.333...

Answer:

10/3

Step-by-step explanation:

-15+6f=5

6f=5-(-15)

6f=5+15

6f=20

f=20/6

simplify

f=10/3

A doctor asks a nurse to give a
patient 250 mg (milligrams) of the
drug Simethicone. The drug is
available only in a solution whose
concentration is 40 mg Simethicone
per 0.6 ml (milliliter) of solution.
How many milliliters of solution
should the nurse give the patient?

Answers

Answer:

Hey there!

For this question, we write a proportion.

[tex]\frac{40}{0.6}=\frac{250}{x}[/tex]

[tex]40x=150[/tex]

[tex]x=3.75[/tex]

Thus, the nurse to give the patient exactly 3.75 ml of the solution.

Let me know if this helps :)

The volume of the simethicone solution given by a nurse is 3.75 milliliters.

Given:

Doctor asks a nurse to give a  patient 250 milligrams of the  drug Simethicone.The concentration of a drug is 40 mg of Simethicone per 0.6 mL.

To find:

The milliliters of a solution to be given to the patient by a nurse.

Solution:

Mass of simethicone drug to be given = 250 mg

Let the volume of the solution with 250 mg of simethicone be x.

The concentration of simethicone in solution = 40 mg/0.6 mL

Mass of simethicone in 1 mL of solution:

[tex]40 mg/0.6 mL=\frac{40 mg}{0.6 mL}\\\\=\frac{400 mg}{6 mL}[/tex]

The mass of simethicone in 'x' mL of solution:

[tex]250 mg=x\times \frac{400 mg}{6 mL}\\\\x=\frac{250 mg\times 6 mL}{400 mg}\\\\x=3.75 mL[/tex]

The volume of the simethicone solution given by a nurse is 3.75 milliliters.

Learn more about the unitary method here:

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Find all real zeros of the function.
g(x) = 2x (x - 5)2(x – 9)?
If there is more than one answer, separate them with commas.
zero(s):

Answers

Answer:

0, 5, 9

Step-by-step explanation:

g(x) = 2x (x - 5)^2(x – 9) = 0

x = 0 or x - 5 = 0 or x - 9 = 0

x = 0 or x = 5 or x = 9

0 5 9
It’s on khan academy

help meplz i want help i bad

Answers

Answer:

.00002

Step-by-step explanation:

2 * 10 ^-5

Move the decimal 5 places to the left since the exponent is negative

2.

We will need to add zeros on the left  Add 4 zeros since we can move it one place already

.00002

Answer:

(D) 0.00002

Step-by-step explanation:

Let's first forget about the 2 in the expression and focus on [tex]10^{-5}[/tex].

If we have 10 to a positive number, that many times the decimal place will move to the right. It's the opposite for 10 to the power of a negative number.

The decimal place will move 5 places to the LEFT.

So:

[tex]0000010\\\\0.00001[/tex]

Now we remember the two, and multiply this by two to get 0.00002.

Hope this helped!

Which fraction is equivalent to -0.12? A. -3/25 B. -7/50 C. 4/25 D. -6/25 Please show ALL work! <3

Answers

Answer:

[tex]\huge\boxed{-\frac{3}{25} }[/tex]

Step-by-step explanation:

-0.12 in fraction form can be written as:

=> - 12/100

=> - 6 / 50

=> - 3/25

Answer:

[tex]\large \boxed{\mathrm{A. \ -3/25}}[/tex]

Step-by-step explanation:

Convert the decimal to a fraction.

-(0.12) = -(12/100)

Simplify the fraction.

-(12/100) = -(6/50) = -(3/25)

if f(x) -3 and g(x) = 3x2+x-6, find (f+9)(x).
A. 4x2 - 9
B. 3x2 + x - 3
C. 3x2 + 2X-9
D. 3x2 - 4x = 3

Answers

Answer:

3x^2 +x -3

Step-by-step explanation:

f(x)= 3 and g(x) = 3x^2+x-6

f+g (x) =  3+  3x^2+x-6

Combine like terms

          = 3x^2 +x -3

3x^2+x-3
I hope this helps

HELPP (ESPECIALLY PART B) Answer the questions in this part of the task based on your understanding of the definition and the standard equation for the conic you chose. part a Inspect the equation for the type of conic section you chose. What attributes are necessary to graph it? Be sure to include specific points or equations to complete your answer. part b Explain how, if you have the attributes given below for the conic you chose, you can derive its equation in standard form.

Answers

The conic section chosen is a parabola, and the attributes for graphing of

a parabola as well as the standard form of the equation are as follows;

Part A: The attribute necessary to graph the equation of the parabola are three points, including, the vertex, the y-intercept and the image of the reflection of the y-intercept across the axis of symmetry.

Part B: The equation in standard form is x = -0.25·y² + y + 3

Reasons:

Part A:

The equation of the conic section of a parabola is; (x - 3)² = 12·(y - 2)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where (h, k) = The vertex

Rearranging the given equation gives;

(x - 3)² = 12·y - 24

12·y - 24 = (x - 3)²

12·y = (x - 3)² + 24

[tex]\displaystyle y = \frac{1}{12} \cdot \left(x - 3\right)^2 + \frac{24}{12} = \frac{1}{12} \cdot \left(x - 3\right)^2 + 2[/tex]

[tex]\displaystyle y = \frac{1}{12} \cdot \left(x - 3\right)^2 + 2[/tex]

Therefore, the vertex of the parabola, (h, k) = (3, 2)

At the y-intercept, x = 0, which gives;

[tex]\displaystyle y = \frac{1}{12} \cdot \left(0 - 3\right)^2 + 2 = \frac{9}{12} + 2 = 2+\frac{3}{4}[/tex]

[tex]\displaystyle y = 2+\frac{3}{4} = 2.75[/tex]

The y-intercept = (0, 2.75)

The x-intercept is given at the point where y = 0, which gives;

(x - 3)² = 12·(0 - 2) = -24

x - 3 = √(-24) = An imaginary number

Therefore, the graph has no x-intercept

Given that a parabola is symmetrical about the vertex, we have a third

point on the parabola at the image of the y-intercept reflected across the

axis of symmetry as follows;

The y-intercept (0, 2.75) is 3 units to the left of the axis of symmetry, x = 3,

therefore, the third point will be 3 units to the right of the axis of symmetry

at the point (3 + 3, 2.75) = (6, 2.75)

Therefore, using the three points, (0, 2.75), (3, 2), and (6, 2.75), the curve

representing the parabola, (x - 3)² = 12·(y - 2), can be drawn.

Please find attached the graph of the parabola created with MS Excel

Part B; Given the attributes of the parabola; Vertex: (4, 2) and focus: (3, 2), we have;

The focus of a parabola is the point (h + p, k)

Where, (h, k) = The vertex

Therefore, by comparison, we have;

(h, k) = (4, 2)

h + p = 3

Therefore;

4 + p = 3

p = 3 - 4 = -1

The vertex form of the equation of the parabola is; (y - k)² = 4·p·(x - h)

Therefore, we get;

(y - 2)² = 4 × (-1) × (x - 4) = -4·(x - 4)

y² - 4·y + 4 = 16 - 4·x

4·x = 16 - (y² - 4·y + 4) = -y² + 4·y + 12

Which gives, the standard form as follows;

[tex]\displaystyle x = -\frac{y^2}{4} + y + 3 = -0.25 \cdot y^2 + y + 3[/tex]

Standard form of the the equation of the parabola; x = -0.25·y² + y + 3

Learn more about the graph of a parabola here:

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Which of the following represents continuous data? A. Amount of coins in your pocket B. Time it takes to count the coins in your pocket C. Number of collector coins you own D. Value of the coins in your pocket

Answers

Answer:

Time it takes to count the coins in your pocket

Step-by-step explanation:

answer is b. time it takes to count coins in your pocket

A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 4x − 3 and EC = 2x + 6, find the distance between the top and bottom of the bridge, in feet.

Answers

Answer:

Total distance = 30 m

Step-by-step explanation:

Given:

AC : EC = 1:1

AC = 4x − 3 and EC = 2x + 6

Find:

Total distance

Computation:

AC = EC

So,

4x - 3 = 2x + 6

2x = 9

x = 4.5

AC = 4(4.5) - 3 = 15 m

EC = 2(4.5) + 6 = 15 m

Total distance = AC + EC

Total distance = 15 m + 15 m

Total distance = 30 m

The distance between the top and bottom of the bridge, in feet, is 15 + 15 = 30m

Given that a new bridge structure requires triangles that are in a ratio of 1:1 with the following parameters

AC = 4x - 3

EC = 2x + 6

Since the measure are in the same ratio, henec;

AC = EC

4x - 3 = 2x + 6

4x - 2x = 6 + 3

2x = 9

x = 4.5

Get the

AC = EC = 4x - 3

AC = EC = 4(4.5) - 3 = 15feet

The distance between the top and bottom of the bridge, in feet, is 15 + 15 = 30m\

Learn more here: https://brainly.com/question/17247176

The members of a film crew are at least 75 miles from their camp and must carry equipment back to camp before a storm arrives. The storm is scheduled to begin in 24 hours. They plan to travel as far as possible by truck and then walk the rest of the way. The truck can travel at a rate of 10 miles per hour through the terrain, and the team can travel 2 miles per hour on foot. Which system represents the number of hours the crew can travel by truck, x, and on foot, y, to reach camp before the storm? x + y < 24 2x + 10y ≥ 75 x + y > 24 2x + 10y ≥ 75 x + y < 24 10x + 2y ≥ 75 x + y > 24 10x + 2y ≥ 75

Answers

Answer:

I DONT UNDERSTAND ANY OF THIS

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

help me plz i wnt help plz i want help

Answers

Answer:

C)28in

Step-by-step explanation:

To get the area of this face, we will divide it into 3 sections.

Area of the 1st section:

Given:

l=4in

w=2in

Formula:

a=l*w

Solution:

a=l*w

a=8in^2

Area of the 2nd section:

Given:

l=2in

w=2in

Formula:

a=l*w

Solution:

a=l*w

a=2in*2in

a=4in^2

Area of the 3rd section:

l=8in

w=2in

Formula:

a=l*w

Solution:

a=l*w

a=8in*2in

a=16in^2

a1+a2+a3=Area of the face

8in^2+4in^2+16in^2=28in^2

Hope this helps ;) ❤❤❤

The answer is c, 28 in. I hope this helps

Town B is 250 km from town A on a bearing of 080°.
Town C is 250 km from town B on a bearing of 220°.
What is the bearing from town A to town C?

Answers

Answer:

Step-by-step explanation:

220-80
The answer would be 140

WILL GIVE BRAINLY PLEASE HELP!!!!
A quadratic equation of the form 0=ax2+bx+c has a discriminant value of -16. How many real number solutions does the equation have?
A) -1
B) 0
C) 1
D) 2

Answers

Answer:

the answer is c. One real number solution

Step-by-step explanation:

Hey There!!

I think the best answer will be is (D) 2.

Because, The discriminant is the expression b2 - 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. Based upon the sign of the expression, you can determine how many real number solutions the quadratic equation has. If you get a positive number, the quadratic will have two unique solutions. Im not a 100% sure this right... Hope This helps!! By ~♡Itsbrazts~♡

Write the equation for the following table:
0 2
1 7
2 13
3 20

Answers

Answer:

Step-by-step explanation:

for each positive integer m, so that la - r2m-ll and la - r2m I are both less than

1 1

Ir2m - r2m-ll .:::: 42(m-l) Ir2 - rll = 24m - 3 ·

It follows that limn--->oo rn = limn--->oo rn-l = a. Taking limits in the recursion in

(d) leads to

1

a=I+--

l+a

which reduces to a 2 = 2. Since rn > 0 for each n, a > O.

Please help On this question

Answers

Answer:

202.5 cm^2

Step-by-step explanation:

We can calculate the area of the shape by completing it

to a full rectangle or dividing it to a rectangle and triangle.

The second way seems easier

The area of the rectangle is calculated by multiplying length to width

20 × 9 = 180 cm^2

The area of a triangle is calculated by multiplying height to the base and that divided by two

5 × 9 ÷ 2 = 22.5 cm^2

Now add these two 180 + 22.5 = 202.5 cm^2

Answer:

202.5 cm squared

Step-by-step explanation:

To find the area of this figure easier, you can cut the figure like I showed in the attachment below.

The rectangle (purple): 20 times 9 is 180.

The right triangle (light blue): 9 times 5 times 1/2 is 22.5.

All together: 180 plus 22.5 is 202.5 cm squared!

Hope that helps and maybe earns a brainliest!

Have a great day! :)

Circles
1. RS and ST are tangent lines. Find the value of x.
R
9x - 30
c.
S
3x
T

Answers

Answer:

x = 15

Step-by-step explanation:

9x-30 = 3x (tangent lines are congruent)

- move the variables to one side

9x-3x=30

6x=30

x=5

--------------

9(5)-30=3(15)

45-30=15

15=15

Done!

The Answer is for this is:
x = 15

Write as an inequality. "Four more than half a number is at most sixteen"

Answers

1/2 + 4 ≤ 16

four more = +4

half a number = 1/2

at most means less or greater which is ≤

Answer:

0.5n + 4 ≤ 16

Step-by-step explanation:

add 4 to half of the unknown number (n). It is at most 16 (less than or equal to).

0.5n + 4 ≤ 16

A shop sells “Gello” pens and “Inko” pens. A “Gello” pen costs £5 and an “Inko” pen costs £7. One day the shop sold 17 pens and recieved £109. How many of each type of pen were solved? Form a pair of simultaneous equations to solve this question.

Answers

Answer:

5 Gello Pens and 12 Inko Pens.

12 Inko Pens adds up to 84.

5 Gello Pens adds up to 25.

84 + 25 = 109.

I hoped this helped :)

5 hello pens and 12 inko pens

help plz help me .me no good

Answers

Answer:

50,000,000

Step-by-step explanation:

5 * 10 ^7

The 7 in the exponent means move the decimal 7 places to the right

5.  We need to add 7 zeros

50000000

50,000,000

Is the first option the answer?!?

A deli sandwich shop is offering either a ham or turkey sandwich, either tomato or vegetable soup, and either coffee or milk for their lunch special. What is the probability that a customer will choose vegetable soup as part of the chosen combination? A. 1/4 B.1/3 C.1/2 D.1/6

Answers

Answer:

1/2

Step-by-step explanation:

answer: 1/2

explaination:
there’s two choices of soup

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. x 2 + 13x + 36

Answers

Step-by-step explanation:

of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. x 2 + 13x + 36

Answer:

you change your mind, drag the item to the trashcan. Click the trashiecan to clear all your answers. Factor completely and then place the factors in the proper location on the grid.

Step-by-step explanation:

Thanks!

cqn someone answer this?​

Answers

Answer:

-3

Step-by-step explanation:

-11/2+27/4+(-17/4)(-22+27-17)/4(-12)/4-3

The anwser to your question would be negative 3

Draw a net of the triangular prism and label each face with its surface area. Use the net of the three-dimensional triangular prism to find the surface area of the solid. 13 points

Answers

Answer:

300 yards squared

Step-by-step explanation:

Triangle area = 12 x 5 / 2 = 30

2 Triangles (because there are two of them) = 60

Big rectangle = 8 x 13 = 104

Small Rectangle = 8 x 5 = 40

Medium Rectangle = 96

Add all up = 300

Hope that helped!!! k

300 yards squared,, I need to answer questions to be able to ask some more

plz help me i need help

Answers

4 x 10^-7 x 2 = 8 x 10^-7
Therefore, 2 times as long.
Answer = 2 times as longer

Explanation:

8 x 10^-7 = (2)4 x 10^-7

Vertex Form y=a(x-h)^2+k what does each variable represent if they were in a problem.

Answers

a represents the step pattern

h represents the x coordinate of the vertex (don’t forget that the - sign changes weather the number is + or -)

k represents the y coordinate of the vertex

Kate wants to paddle
her canoe across the lake. To determine how far she must paddle, she paced out a triangle,counting the number of strides, as shown.
If Kate's strides average 3.5 ft, what is the
length of the longest side of the triangle?
What distance must Kate paddle across
the lake? ​

Answers

Answer:

1. Length of longest side of the triangle = 1,050 ft

2. Length = 437.5 ft

Step-by-step explanation:

Given:

Kate's strides average = 3.5 ft

Find:

1.longest side of the triangle

2.Distance must Kate paddle across the lake

Computation:

1.longest side of the triangle

longest side of the triangle = AE

So,

longest side of the triangle = 150 + 150

longest side of the triangle = 300

Length of longest side of the triangle = 300 × 3.5 ft

1. Length of longest side of the triangle = 1,050 ft

2.Distance must Kate paddle across the lake.

We know that,

ΔABD ~ ΔACE

So,

AB / AC = BD / CE

80 / 160 = BD / 250

BD = 125 Strides

Length = 125 × 3.5 ft

2. Length = 437.5 ft

the answer is in the attached image

5.4(m-2)= -2(3m+3) please help asap

Answers

Answer:

m = 0.421

Step-by-step explanation:

5.4(m-2)= -2(3m+3)     (expand parentheses by distributive property)

m(5.4) -2(5.4) = 3m(-2) + 3(-2)

5.4m - 10.8 = -6m - 6      (add 6m to both sides)

5.4m - 10.8 + 6m =  - 6

11.4m - 10.8 =  - 6   (add 10.8 to both sides)

11.4m = -6 + 10.8

11.4m = 4.8   (divide both sides by 11.4)

m = 4.8 / 11.4

m = 0.421

Answer:

m = 8/19

Step-by-step explanation :

5.4  (m-2) = -2 (3m +3)  

54/10 (m-2) = (3m +3)   as n = 1

2.3^3 /  2.5  (m-2) = (3m + 3)

4.868 (m-2) = (3m +3)

4.868 + 3 = (3m^2 * m-2)

8 / 9.5 * 2  

m = 8 / 19

Other Questions
Explain the role and function of the committees of correspondence. HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Jamie was participating in a market research study regarding computers when he was presented with 24 different computers that varied on four criteria. He was asked to rank all 24 descriptions in terms of his preference for those combinations of features. Which approach to assess the relative importance Jamie places on evaluative criteria was this research using? Jessie and Paul have worked in the same office at DEF Insurance LLC for 6 years. Jessie has always taken extra care to follow the office norms and ensure that everyone has a happy and harmonious working experience. Paul has been very driven during his years at DEF Insurance, and though he started as an insurance agent, he has since been promoted to the agency manager and proudly displays all of his awards on the wall of his new office. According to Learned Needs Theory, Jessie most likely has a high: Group of answer choices Find interval of increase and decrease of f(x) = 8 sin(x) + cot(x), x The following information is for the standard and actual costs for the Happy Corporation: Enter favorable variances as negative numbers. Standard Costs: Budgeted units of production - 16,000 [80% (or normal) capacity] Standard labor hours per unit - 4 Standard labor rate - $26 per hour Standard material per unit - 8 lbs. Standard material cost - $12 per pound Standard variable overhead rate - $15 per labor hour Budgeted fixed overhead - $640,000 Fixed overhead rate is based on budgeted labor hours at 80% (or normal) capacity.Actual Cost:Actual production - 16,500 unitsActual fixed overhead - $640,000Actual variable overhead - $1,000,000Actual labor - 65,000 hours, total labor costs $1,700,000Actual material purchased and used - 130,000 lbs, total material cost $1,600,000Actual variable overhead - $1,000,000Determine the Quantity Variancea. 24,000 unfavorableb. 24,000 favorablec. 12,000 unfavorabled. 12,000 favorable If mowing burns average $115 over 20 minutes how many calories are you burning in one hour Find all real zeros of the function.g(x) = 2x (x - 5)2(x 9)?If there is more than one answer, separate them with commas. zero(s): Atoms contain positive and negative charges. Why is the overall charge on an atom neutral?A. Atoms contain the same amount of protons and electrons, and their charges cancel out.B. The nucleus of an atom contains neutrons, which keep the positive and negative charges balanced.C. Atoms are all negatively charged because electrons are on the outside of the atom.D. Atoms contain the same amount protons and neutrons, and their charges cancel out. Which statements about command economic systems are false? Select all that apply.(Multiple choice btw)Prices are set by the government.Supply and demand are the basis for economic decisions.People's jobs are chosen by the government.Businesses are driven by profit. f(x)=x^2 what is g(x)?pls help me I need some help with simplifying expressions, please. 8y - 9y = Identify the three mistakes and type the correct answers.She was found guilty for murder and was sentenced too a long period of inprisonment.Someone find the mistakes please Aug 19,7:01:38 PMKylie is moving and must rent a truck. There is an initial charge of $50 for the rentalplus a fee of $3 per mile driven. Make a table of values and then write an equation forC, in terms of m, representing the total cost of renting the truck if Kylie were todrive m miles.Number of Miles Driven Total Cost to Rent Truck The table shows the probability distribution of student ages in a high schoolwith 1500 students. What is the expected value for the age of a randomlychosen student?Age131415161718Probability 0.01 0.23 0.26 0.28 0.20 0.02 Possible Points: 100 One January day, the low temperature in Fargo, ND was -8 degrees. Over a period of six hours, the temperature rose 4 degrees per hour. After si hours, what was the temperature? A 5.0 kg block hangs from a spring with spring constant 2000 N/m. The block is pulled down 5.0 cm from the equilibrium position and given an initial velocity of 1.0 m/s back towards equilibrium. a) What is the total mechanical energy of the motion Supply Chain Integration Supply chain integration is a major contributing factor to organizational success. The goal of supply chain integration is alignment within the supply chain. As a business leader, how can you achieve greater supply chain integration with suppliers and customers Which is the correct replacement for the underlined portion of the sentence below?The flashing Hollywood lights could be seen over a much great distance than the small city lights. Group of answer choicesgreat muchgreatestmost greatestmuch greater Does someone know how to solve this?